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Nested invariant tori foliating a vector field and its curl: Toward MHD equilibria and steady Euler flows in toroidal domains without continuous Euclidean isometries
http://hdl.handle.net/10655/0002000032
http://hdl.handle.net/10655/00020000326344598d-1956-40e4-b9fc-07ee3148da4d
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13902_J. Math. Phys.pdf (1.6 MB)
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VoR_J.Math.Phys.64_081505.pdf (10.6 MB)
Download is available from 2024/8/10.
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Item type | 学術雑誌論文 / Journal Article(1) | |||||||||
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公開日 | 2023-08-29 | |||||||||
タイトル | ||||||||||
言語 | en | |||||||||
タイトル | Nested invariant tori foliating a vector field and its curl: Toward MHD equilibria and steady Euler flows in toroidal domains without continuous Euclidean isometries | |||||||||
言語 | ||||||||||
言語 | eng | |||||||||
資源タイプ | ||||||||||
資源タイプ識別子 | http://purl.org/coar/resource_type/c_6501 | |||||||||
資源タイプ | journal article | |||||||||
著者 |
SATO, Naoki
× SATO, Naoki
× YAMADA, Michio
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著者ID | ||||||||||
内容記述 | ORCID 0000-0002-2973-0635 | |||||||||
抄録 | ||||||||||
内容記述タイプ | Abstract | |||||||||
内容記述 | This paper studies the problem of finding a three-dimensional solenoidal vector field such that both the vector field and its curl are tangential to a given family of toroidal surfaces. We show that this question can be translated into the problem of determining a periodic solution with periodic derivatives of a two-dimensional linear elliptic second-order partial differential equation on each toroidal surface and prove the existence of smooth solutions. Examples of smooth solutions foliated by toroidal surfaces that are not invariant under continuous Euclidean isometries are also constructed explicitly, and they are identified as equilibria of anisotropic magnetohydrodynamics. The problem examined here represents a weaker version of a fundamental mathematical problem that arises in the context of magnetohydrodynamics and fluid mechanics concerning the existence of regular equilibrium magnetic fields and steady Euler flows in bounded domains without continuous Euclidean isometries. The existence of such configurations represents a key theoretical issue for the design of the confining magnetic field in nuclear fusion reactors known as stellarators. | |||||||||
言語 | en | |||||||||
書誌情報 |
en : Journal of Mathematical Physics 巻 64, 号 8, p. 081505, 発行日 2023-08-11 |
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出版者 | ||||||||||
言語 | en | |||||||||
出版者 | AIP Publishing | |||||||||
ISSN | ||||||||||
収録物識別子タイプ | ISSN | |||||||||
収録物識別子 | 0022-2488 | |||||||||
書誌レコードID | ||||||||||
収録物識別子タイプ | NCID | |||||||||
収録物識別子 | AA00701758 | |||||||||
DOI | ||||||||||
関連タイプ | isVersionOf | |||||||||
識別子タイプ | DOI | |||||||||
関連識別子 | https://doi.org/10.1063/5.0151955 | |||||||||
権利 | ||||||||||
言語 | en | |||||||||
権利情報 | This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in J. Math. Phys. 64, 081505 (2023) and may be found at https://doi.org/10.1063/5.0151955. Copyright 2023 Author(s). This article is distributed under a Creative Commons Attribution (CC BY) License. | |||||||||
情報源 | ||||||||||
言語 | en | |||||||||
関連名称 | Naoki Sato, Michio Yamada; Nested invariant tori foliating a vector field and its curl: Toward MHD equilibria and steady Euler flows in toroidal domains without continuous Euclidean isometries. J. Math. Phys. 1 August 2023; 64 (8): 081505. https://doi.org/10.1063/5.0151955 | |||||||||
関連サイト | ||||||||||
識別子タイプ | DOI | |||||||||
関連識別子 | https://doi.org/10.1063/5.0151955 | |||||||||
関連名称 | Publisher version | |||||||||
著者版フラグ | ||||||||||
出版タイプ | AM | |||||||||
出版タイプResource | http://purl.org/coar/version/c_ab4af688f83e57aa | |||||||||
NAIS | ||||||||||
13902 |